Answer
The given sequence is neither a geometric sequence nor arithmetic sequence.
Work Step by Step
The given general term is $a_{n}$ = $n^{2}$ + 5
First term $a_{1}$ = $1^{2}$ + 5 = 6 (if n=1)
Second term $a_{2}$ = $2^{2}$ + 5 = 9 (if n=2)
Third term $a_{3}$ = $3^{2}$ + 5 = 14 (if n=3)
Forth term $a_{4}$ = $4^{2}$ + 5 = 21 (if n=4)
Ratio of consecutive terms.
$\frac{21}{14}$ = $\frac{3}{2}$.
$\frac{14}{9}$ = $\frac{14}{9}$.
$\frac{9}{6}$ = $\frac{3}{2}$.
Difference of consecutive terms
21 - 14 = 7
14 - 9 = 5
9 - 6 = 3
From above we observe that neither the ratio nor the difference of two consecutive terms is constant. So the given sequence is neither a geometric sequence nor arithmetic sequence.
